The Energy Networks Association (ENA) said about 3,000 homes across the UK are without electricity following the bad weather, as one of the UK's biggest power distributors promised to almost triple compensation for customers affected.

UK Power Networks, which owns electricity lines and cables in London, the South East and east of England, said it will increase payments for 48 to 60-hour outages from £27 to £75 for those affected on Christmas Day as "a gesture of goodwill".

Additional payments will be made to customers who have been without electricity for longer than that time - up to a maximum of £432.

Meanwhile, Northern Power Grid, which delivers electricity across the North East and Yorkshire, tweeted that 2,000 customers were without power tonight.

Investigators were searching for the cause of the power outage, although it is not believed to be weather related, a spokesman said.

Customers in the region are expected to have power returned tonight, he added.

Electricity North West (ENW) said 500 customers were still without power in Cumbria this evening after engineers had restored more than 24,000 properties across the region.

Meanwhile in Wales, 500 properties - mainly in Anglesey and Gwynedd - are waiting for power to be restored following the storms, a spokesman for Scottish Power said.

UK Power Networks said 322 customers in Kent were without power, with 96 in Surrey and 218 in Sussex.

A spokesman for the company said: "Due to the severity of the storm damage it may take until the end of the week to re store power supplies to the final single premises affected in these areas, though work is continuing to reconnect most of the remaining supplies as quickly as possible."

Scottish and Southern Energy (SSE) confirmed 350 homes were without power in south-central England.

A spokeswoman said rural communities affected are in Hampshire, Surrey and West Sussex where flooded ground has made access hard, but it is hoped electricity will be restored by the end of the day.

Despite forecasters predicting a weekend of more settled weather, the Met Office has issued a yellow warning - meaning be aware - for the early hours of Monday morning.

Heavy rain is expected to spread across the south west of England and south Wales from Sunday afternoon into Monday morning, the Met Office said.

Winds of 60-70mph are expected to hit Wales and parts of south-west and southern England, while exposed areas such as the Isles of Scilly, west Cornwall and west Wales could see gales of up to 80mph.

"With ground already saturated over much of this region, the public should be aware of the risk of further local flooding," the Met Office said.

Scotland is also braced for more heavy rain overnight on Sunday into Monday morning, with 20-30mm of rainfall predicted and as much as 50-60mm over high ground.

Met Office forecaster Charlie Powell said the unsettled weather looks set to continue into the new year.

"It certainly looks a very wet and windy picture," he said.

"On New Year's Eve another band of rain will push in from the west. It will be a dry start to Wednesday but the unsettled weather will be around for quite some time into the new year."

The Environment Agency (EA) said the predicted rainfall meant there is a "continued heightened flood risk" across southern England, especially south-west England where river levels remain high and the ground is already saturated.

Large rivers such as the Thames, Severn and Great Ouse in Cambridgeshire are most at risk of flooding, while high water levels on the River Medway and Stour in Kent will cause continued flooding and travel disruption, the EA said.

Some 1,300 properties have been flooded during the recent storms in England, the EA said, while flood defences have protected more than 80,000 properties.

Craig Woolhouse, the EA's head of flood incident management, said: "Our thoughts are with those who have been affected by flooding over Christmas. Our teams remain out on the ground working around the clock to protect communities from flooding.

"With more wet weather expected early next week we are monitoring rivers and working to protect communities from flooding with our partners in the emergency services and local authorities.

"We urge people to stay safe and avoid driving or walking through flood water and visit the Environment Agency website for advice and sign up for flood warnings."

A Downing Street spokesman said ministers held a COBRA meeting today where it was agreed financial assistance will be given to local authorities facing an undue financial burden because of the storms through a process known as the Bellwin scheme.

Energy Secretary Edward Davey is also in talks with UK Power Networks to insist on a clear public timeline for work to get power back on, he added.

The spokesman said: "Crucially the Government is pushing councils to have a clear plan for if they face flooding over the new year.

"The Environment Agency, the cabinet office and the Department for Communities and Local Government are working together to ensure councils are best prepared for further bad weather and will be contacting councils to make sure they are going to be manned over New Year to help people."

Environment minister Dan Rogerson is in talks with insurance companies and the Association of British Insurers, while the Government has asked EA representatives on the ground to identify which insurance companies are not moving fast enough, the spokesman said.

Prime Minister David Cameron, who was yesterday confronted by an angry flood victim in Yalding, Kent, tweeted: "I've asked the Dept for Communities & Local Govt to ensure councils have robust plans in case of bad weather and flooding over New Year."

The EA said its teams will remain on duty to operate pumping stations, issue flood warnings and check that flood banks, walls and barriers are working effectively.

Some 73 flood alerts and 14 more serious flood warnings remained in place across the country this evening.